{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SciPy基础"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.1 SciPy概述"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.1.2 安装SciPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy\n",
    "import numpy as np\n",
    "import matplotlib as mpl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.2 SciPy基础"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.2.2基础函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.2.3 特殊函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import special\n",
    "def drumhead_height(n, k, distance, angle, t):\n",
    "    kth_zero = special.jn_zeros(n, k)[-1]\n",
    "    return np.cos(t) * np.cos(n*angle) * special.jn(n, distance*kth_zero)\n",
    "theta = np.r_[0:2*np.pi:50j]\n",
    "radius = np.r_[0:1:50j]\n",
    "x = np.array([r * np.cos(theta) for r in radius])\n",
    "y = np.array([r * np.sin(theta) for r in radius])\n",
    "z = np.array([drumhead_height(1, 1, r, theta, 0.5) for r in radius])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "fig = plt.figure()\n",
    "ax = Axes3D(fig)\n",
    "ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap=cm.jet)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.3 积分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9999999999999999, 1.1102230246251564e-14)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.integrate import quad\n",
    "res,err = quad(np.sin, 0, np.pi/2)\n",
    "res, err"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(err, 1 - res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_derivative(ypos, time, counter_arr):\n",
    "    counter_arr += 1\n",
    "    return -2 * ypos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "counter = np.zeros((1,), dtype=np.uint16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import odeint\n",
    "time_vec = np.linspace(0, 4, 40)\n",
    "yvec, info = odeint(calc_derivative, 1, time_vec,\n",
    "                    args=(counter,), full_output=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([258], dtype=uint16)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([31, 35, 43, 49, 53, 57, 59, 63, 65, 69], dtype=int32)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "info['nfe'][:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass = 0.5  # kg\n",
    "kspring = 4  # N/m\n",
    "cviscous = 0.4  # N s/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eps = cviscous / (2 * mass * np.sqrt(kspring/mass))\n",
    "eps < 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "nu_coef = cviscous / mass\n",
    "om_coef = kspring / mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_deri(yvec, time, nuc, omc):\n",
    "    return (yvec[1], -nuc * yvec[1] - omc * yvec[0])\n",
    "\n",
    "time_vec = np.linspace(0, 10, 100)\n",
    "yarr = odeint(calc_deri, (1, 0), time_vec, args=(nu_coef, om_coef))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.4 插值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "measured_time = np.linspace(0, 1, 10)\n",
    "noise = (np.random.random(10)*2 - 1) * 1e-1\n",
    "measures = np.sin(2 * np.pi * measured_time) + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import interp1d\n",
    "linear_interp = interp1d(measured_time, measures)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "computed_time = np.linspace(0, 1, 50)\n",
    "linear_results = linear_interp(computed_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "cubic_interp = interp1d(measured_time, measures, kind='cubic')\n",
    "cubic_results = cubic_interp(computed_time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.5 傅里叶变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_step = 0.02\n",
    "period = 5.\n",
    "time_vec = np.arange(0, 20, time_step)\n",
    "sig = np.sin(2 * np.pi / period * time_vec) + \\\n",
    "       0.5 * np.random.randn(time_vec.size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import fftpack\n",
    "sample_freq = fftpack.fftfreq(sig.size, d=time_step)\n",
    "sig_fft = fftpack.fft(sig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "pidxs = np.where(sample_freq > 0)\n",
    "freqs = sample_freq[pidxs]\n",
    "power = np.abs(sig_fft)[pidxs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freq = freqs[power.argmax()]\n",
    "np.allclose(freq, 1./period)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "sig_fft[np.abs(sample_freq) > freq] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "main_sig = fftpack.ifft(sig_fft)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Amplitude')"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab as plt\n",
    "plt.figure()\n",
    "plt.plot(time_vec, sig)\n",
    "plt.plot(time_vec, main_sig, linewidth=3)\n",
    "plt.xlabel('Time [s]')\n",
    "plt.ylabel('Amplitude')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.6 线性代数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.7 统计学"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.8 函数优化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.8.1 寻找标量函数的最小值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x**2 + 10*np.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-10, 10, 0.1)\n",
    "plt.plot(x, f(x))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: -7.945823\n",
      "         Iterations: 5\n",
      "         Function evaluations: 18\n",
      "         Gradient evaluations: 6\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-1.30644012])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fmin_bfgs(f, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.83746709])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fmin_bfgs(f, 3, disp=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.30641113])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid = (-10, 10, 0.1)\n",
    "xmin_global = optimize.brute(f, (grid,))\n",
    "xmin_global"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.8374671194983834"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xmin_local = optimize.fminbound(f, 0, 10)    \n",
    "xmin_local"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.8.2 寻找标量函数的根"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "root = optimize.fsolve(f, 1)  # 我们的最初猜想是1\n",
    "root"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.47948183])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "root2 = optimize.fsolve(f, -2.5)\n",
    "root2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.8.3 曲线拟合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "xdata = np.linspace(-10, 10, num=20)\n",
    "ydata = f(xdata) + np.random.randn(xdata.size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f2(x, a, b):\n",
    "    return a*x**2 + b*np.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.99707487, 10.1306459 ])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "guess = [2, 2]\n",
    "params, params_covariance = optimize.curve_fit(f2, xdata, ydata, guess)\n",
    "params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.9 信号处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import signal\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24bc9bce668>]"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0, 5, 100)\n",
    "x = t + np.random.normal(size=100)\n",
    "\n",
    "plt.plot(t, x, linewidth=3)\n",
    "plt.plot(t, signal.detrend(x), linewidth=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24bc9964c50>]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0, 5, 100)\n",
    "x = np.sin(t)\n",
    "\n",
    "plt.plot(t, x, linewidth=3)\n",
    "plt.plot(t[::2], signal.resample(x, 50), 'ko')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.10 图形处理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.10.1 图像的几何变换 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "module 'scipy.misc' has no attribute 'lena'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-85-57569faee535>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmisc\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mpl\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mlena\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmisc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlena\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[0mshifted_lena\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mndimage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshift\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlena\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m50\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m50\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mshifted_lena2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mndimage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshift\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlena\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m50\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m50\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'nearest'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: module 'scipy.misc' has no attribute 'lena'"
     ]
    }
   ],
   "source": [
    "from scipy import misc\n",
    "import matplotlib.pyplot as pl\n",
    "lena = misc.lena()\n",
    "shifted_lena = ndimage.shift(lena, (50, 50))\n",
    "shifted_lena2 = ndimage.shift(lena, (50, 50), mode='nearest')\n",
    "rotated_lena = ndimage.rotate(lena, 30)\n",
    "cropped_lena = lena[50:-50, 50:-50]\n",
    "zoomed_lena = ndimage.zoom(lena, 2)\n",
    "zoomed_lena.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'subplot' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-86-707631d9e9a2>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0msubplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m151\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mpl\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mimshow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mshifted_lena\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcmap\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mcm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgray\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'off'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'subplot' is not defined"
     ]
    }
   ],
   "source": [
    "subplot(151)\n",
    "pl.imshow(shifted_lena, cmap=cm.gray)\n",
    "axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.10.2 图像滤波器"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'ndimage' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-87-860d10518de2>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mel\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mndimage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgenerate_binary_structure\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mel\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'ndimage' is not defined"
     ]
    }
   ],
   "source": [
    "el = ndimage.generate_binary_structure(2, 1)\n",
    "el"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.10 MATLAB文件读写"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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